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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 6776i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6776.f2 | 6776i1 | \([0, 0, 0, 10285, -114466]\) | \(66325500/41503\) | \(-75289698491392\) | \([2]\) | \(11520\) | \(1.3518\) | \(\Gamma_0(N)\)-optimal |
6776.f1 | 6776i2 | \([0, 0, 0, -42955, -934362]\) | \(2415899250/1294139\) | \(4695339378644992\) | \([2]\) | \(23040\) | \(1.6983\) |
Rank
sage: E.rank()
The elliptic curves in class 6776i have rank \(0\).
Complex multiplication
The elliptic curves in class 6776i do not have complex multiplication.Modular form 6776.2.a.i
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.